User blog:Mush9/Exploding Dimension Realm
Exploding Dimension Realm The following numbers describe steps in computing a notation. 0*. {0, …} => Relating to Knuth’s Arrow Notation. x = ( (cardinality of …) - 1) / 2 x is initially drawn up as the number just left of centre. Nx+1 = (Nx ^Nx+1 Nx+2) Each step, the centre point is redrawn as each central bracket is solved for: 3 ^3 3 *3 3 ^(3 ^3 3) 3 *5 3 ^(3 ^(3 ^3 3) 3) 3 *7 3 ^(3 ^(3 ^(3 ^3 3) 3) 3) 3 *9 ... 1. {..., {N1, N2, …, Nn-1,1}, …} => {..., {N2, …, {N1, N2, …, Nn-1}}, …} 2. {..., {N1, N2, …, Nn}, …} => {..., {N2, …, {N1, N2, …, Nn-1}}, …} 3. {..., {N1, Nn}, ...} => {..., N1, Nn, ...} 4. {..., {N}, ...}, {N} => N 5. {..., {1, N2, …, D', …, Nn}, …} => {..., 1, N2, …, …, Nn, …} 6*. {'D, …, D', …, Nn} => {'D-1, …, …, Nn} ''D describes the main array’s dimension, and is carried forth. It only matters decrementally, and for remerging.'' Examples: {1, 3, 3, 3} => {1, 3, 3, {1, 3, 3, 2}} (2) => {1, 3, 3, {1, 3, 3, {1, 3, 3, 1}}} (2) => {1, 3, 3, {1, 3, 3, {1, 3, 3}}} (1) => {1, 3, 3, {1, 3, 3, {1, 3, {1, 3, 2}}}} (2) => {1, 3, 3, {1, 3, 3, {1, 3, {1, 3, {1, 3, 1}}}}} (2) => {1, 3, 3, {1, 3, 3, {1, 3, {1, 3, {1, 3}}}}} => {1, 3, 3, {1, 3, 3, {1, 3, {1, 3, 1, 3}}}} (3) => {1, 3, 3, {1, 3, 3, {1, 3, 1, 3, 3}}} (5) => {1, 3, 3, {1, 3, 3, 1, 3, 3, 3}} (5) => {1, 3, 3, 1, 3, 3, 3, 3, 3} (5) => {0, 3, 3, 3, 3, 3, 3, 3} (6) => 3 ^(3 ^(3 ^3 3) 3) 3 (0) '' Generally, arrays with N-items equal to D''' are very regressive. Equally, arrays with smaller ranges tend to be regressive. Higher 'D's usually make larger numbers.'' {2, 5, 5} => {2, 5, {2, 5, 4}} => {2, 5, {2, 5, {2, 5, 3}}} => {2, 5, {2, 5, {2, 5, {2, 5, 2}}}} => {2, 5, {2, 5, {2, 5, {2, 5, {2, 5, 1}}}}} => {2, 5, {2, 5, {2, 5, {2, 5, {2, 5}}}}} => {2, 5, {2, 5, {2, 5, {2, 5, 2, 5}}}} => {2, 5, {2, 5, {2, 5, 2, 5, 2, 5}}} => {2, 5, {2, 5, 2, 5, 2, 5, 2, 5}} => {2, 5, 2, 5, 2, 5, 2, 5, 2, 5} => {2, 5, 5, 5, 5, 5} => {1, 5, 5, 5, 5, 5} => {1, 5, 5, 5, 5, {1, 5, 5, 5, 5, 4}} => ... {2, 8, 5, 9} => {2, 8, 5, {2, 8, 5, 8}} => {2, 8, 5, {2, 8, 5, {2, 8, 5, 7}} => … => {2, …, 2, ...} => {1, …, …} => … => {1, …, 1, ...} = {0, …, ...} ''Using another array for the value of '''D is especially powerful.'' {{9, 6, 3, 9}, ...} => … => {{9, 6, 3, 9}, …, {9, 6, 3, 9}, ...} => {{9, 6, 3, 9}, …, ...} => {{9, 6, 3, 9} - 1, …} => … '' Nesting arrays within each other, esecially into the place of D, creates even more powerful structures. '' Category:Blog posts